Fourier expansion along geodesics on Riemann surfaces
Anton Deitmar
Open Mathematics, Tome 12 (2014), p. 559-573 / Harvested from The Polish Digital Mathematics Library
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For an eigenfunction of the Laplacian on a hyperbolic Riemann surface, the coefficients of the Fourier expansion are described as intertwining functionals. All intertwiners are classified. A refined growth estimate for the coefficients is given and a summation formula is proved.

Publié le : 2014-01-01
EUDML-ID : urn:eudml:doc:269044 
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     author = {Anton Deitmar},
     title = {Fourier expansion along geodesics on Riemann surfaces},
     journal = {Open Mathematics},
     volume = {12},
     year = {2014},
     pages = {559-573},
     zbl = {1318.11070},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0366-x}
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Anton Deitmar. Fourier expansion along geodesics on Riemann surfaces. Open Mathematics, Tome 12 (2014) pp. 559-573. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0366-x/

[1] Bernstein J., Reznikov A., Analytic continuation of representations and estimates of automorphic forms, Ann. of Math., 1999, 150(1), 329–352 http://dx.doi.org/10.2307/121105 | Zbl 0934.11023

[2] Bernstein J., Reznikov A., Estimates of automorphic functions, Mosc. Math. J., 2004, 4(1), 19–37 | Zbl 1081.11037

[3] Deitmar A., Invariant triple products, Int. J. Math. Math. Sci., 2006, #48274 | Zbl 1140.22018

[4] Gangolli R., Varadarajan V.S., Harmonic Analysis of Spherical Functions on Real Reductive Groups, Ergeb. Math. Grenzgeb., 101, Springer, Berlin, 1988 http://dx.doi.org/10.1007/978-3-642-72956-0 | Zbl 0675.43004

[5] Gradshteyn I.S., Ryzhik I.M., Table of Integrals, Series, and Products, 7th ed., Elsevier/Academic Press, Amsterdam, 2007 | Zbl 1208.65001

[6] Harish-Chandra, Harmonic analysis on real reductive groups. I. The theory of the constant term, J. Functional Analysis, 1975, 19, 104–204 http://dx.doi.org/10.1016/0022-1236(75)90034-8 | Zbl 0315.43002

[7] Iwaniec H., Spectral Methods of Automorphic Forms, 2nd ed., Grad. Stud. Math., 53, American Mathematical Society, Providence, 2002 | Zbl 1006.11024

[8] Knapp A.W., Representation Theory of Semisimple Groups, Princeton Landmarks Math., Princeton University Press, Princeton, 2001 | Zbl 0993.22001

[9] Molčanov V.F., Tensor products of unitary representations of the three-dimensional Lorentz group, Izv. Akad. Nauk SSSR Ser. Mat., 1979, 43(4), 860–891 (in Russian)

[10] Seeger A., Sogge C.D., Bounds for eigenfunctions of differential operators, Indiana Univ. Math. J., 1989, 38(3), 669–682 http://dx.doi.org/10.1512/iumj.1989.38.38031 | Zbl 0703.35133